Quadratic formula Practice Questions (Grade 9)

Question 1easy

What is the discriminant of $2x^2 + 3x - 5 = 0$ ?

Discriminant $= b^2 - 4ac = 9 - 4(2)(-5) = 9 + 40 = 49$ .

Question 2easy

Solve: $x^2 + 4x + 1 = 0$ .

$a=1, b=4, c=1$ . Discriminant: $16-4=12$ . $x = \dfrac{-4 \pm \sqrt{12}}{2} = -2 \pm \sqrt{3}$ .

Question 3easy

Solve using the quadratic formula: $x^2 - 5x + 6 = 0$ .

$a=1, b=-5, c=6$ . Discriminant: $25-24=1$ . $x = \dfrac{5 \pm 1}{2} = 3, 2$ .

Question 4easy

For the equation $x^{2} - 7x + 10 = 0$ , what is the product of its two solutions?

The solutions are $2$ and $5$ , so the product is $2 \cdot 5 = 10$ (equivalently, $\dfrac{c}{a} = 10$ ).

Question 5easy

Use the quadratic formula to solve $x^{2} - 8x + 15 = 0$ . Enter the larger solution.

$x = \dfrac{8 \pm \sqrt{64 - 60}}{2} = \dfrac{8 \pm 2}{2}$ , so $x = 5$ or $x = 3$ ; the larger solution is $5$ .

Question 6easy

What is the sum of the two solutions of $x^{2} - 7x + 10 = 0$ ?

The equation factors as $(x - 2)(x - 5) = 0$ , so the solutions are $2$ and $5$ and their sum is $2 + 5 = 7$ (equivalently, $-\dfrac{b}{a} = 7$ ).

Question 7easy

For the equation $1x^{2} + 6x + 9 = 0$ , how many real solutions are there?

The discriminant $b^{2} - 4ac = 0$ , so the parabola is tangent to the $x$ -axis: exactly $1$ real solution.

Question 8easy

Solve $x^{2} - 2x - 8 = 0$ using the quadratic formula. Enter the smaller solution.

$x = \dfrac{2 \pm \sqrt{4 + 32}}{2} = \dfrac{2 \pm 6}{2}$ , so $x = 4$ or $x = -2$ ; the smaller solution is $-2$ .

Quadratic formula practice